Recent STM experiments on c-axis tunnelling into a vortex core of YBCO have yielded a sub-gap differential conductance which is not invariant under a reversal of the applied bias. By computing the differential conductance G(E) of a normal-superconducting contact to all orders in the tunnelling strength, we predict that in the absence of open channels in the superconductor, G(E) is necessarily an even function of E and that an asymmetric current-voltage characteristic implies the existence of propagating bound-states within the vortex core.